Question

the speed, \\(s\\), of the current in a certain whirlpool is modeled by \\(s = \frac{300}{d}\\), where \\(d\\) is the distance from the center of the whirlpool. which statement is true?

• as you move closer to the center of the whirlpool, the speed of the current approaches 0.
• as you move closer to the center of the whirlpool, the speed of the current approaches 1.
• as you move closer to the center of the whirlpool, the speed of the current approaches infinity.
• as you move closer to the center of the whirlpool, the speed of the current approaches 300.

Explanation:

Identify the model and variables

Using the Inverse Variation knowledge point

$$ s = \frac{300}{d} $$

where \(s\) is the speed of the current and \(d\) is the distance from the center of the whirlpool.

Analyze the limit behavior as distance decreases

Using the Rational Function Limits knowledge point

$$ \lim_{d \to 0^+} s = \lim_{d \to 0^+} \frac{300}{d} = \infty $$

Match with the correct statement

Using the Inverse Variation and Rational Function Limits knowledge points

$$ d \to 0^+ \implies s \to \infty $$

This matches the statement: "As you move closer to the center of the whirlpool, the speed of the current approaches infinity."

Answer:

• As you move closer to the center of the whirlpool, the speed of the current approaches 0.
• As you move closer to the center of the whirlpool, the speed of the current approaches 1.
• As you move closer to the center of the whirlpool, the speed of the current approaches infinity. (Correct answer)
• As you move closer to the center of the whirlpool, the speed of the current approaches 300.